when I do the pullup portion i alternate my grips palms out (pullup) palms in (chinup) palms faceing each other. I do this because I am still week in the pullup department and can do more in less time this way.That being said, I am going to postulate that this IS a good practice. Changing the grip changes the muscles that are affected. Therefore, changing the grip allows you to more fully work more muscles. I remind myself i am doing this for fitness, not just to increase my number of pullups. It also allows us to work the large back muscles more since when they get fatigued we can change grip so that the arms carry a bigger portion of the load. Changing grips also allows us to get a better arm wrokout because so much more load is carried by the arms during a chinup. Lastly, this enables us to do more volume resulting in a bigger impact on the nervous and cardio vascular system

You can also vary the width of the grip, and you can do similar things with pushups and squats. I think maybe it makes the most sense to use lots of variation during Day 1. On Day 2, maybe use the hardest 1 or 2 variations, or start with the hardest variation and work toward the easiest as you fatigue. On Day 3, you could also work hardest to easiest, or you could just stick with one variation.

i completely agree with the OP as well. i've been varying my grip since the start, but not evenly. i always start with pullups and then alternate sets with chins, but then switch to straight chins when i get tired so i can keep going. i was concerned that my ability to do pullups would lag, but today (wk7/lvl4 day 1) i was able to make 21 sets, alternating the whole way. towards the end i was actually having more trouble with the chins.